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- Warm Up
- 1. Find each angle measure.
- True or False. If false explain.
- 2. Every equilateral triangle is isosceles.
- 3. Every isosceles triangle is equilateral.

60 60 60

True

False an isosceles triangle can have only two

congruent sides.

Isosceles Triangles

- 4.2
- Apply properties of isosceles triangles.

Recall that an isosceles triangle has at least

two congruent sides. The congruent sides are

called the legs. The vertex angle is the angle

formed by the legs. The side opposite the vertex

angle is called the base, and the base angles are

the two angles that have the base as a side.

3 is the vertex angle. 1 and 2 are the base

angles.

4-1

4-3

Theorem 4-2

- The bisector of the vertex of an isosceles

triangle is the perpendicular bisector of the

base

Example 1 Astronomy Application

The mYZX 180 140, so mYZX 40.

Since YZX X, XYZ is isosceles by the

Converse of the Isosceles Triangle Theorem.

Thus YZ YX 20 ft.

Example 2 Finding the Measure of an Angle

Find mF.

mF mD x

Isosc. Thm.

mF mD mA 180

Sum Thm.

Substitute the given values.

x x 22 180

Simplify and subtract 22 from both sides.

2x 158

Divide both sides by 2.

x 79

Thus mF 79

Example 3 Finding the Measure of an Angle

Find mG.

mJ mG

Isosc. Thm.

Substitute the given values.

(x 44) 3x

Simplify x from both sides.

44 2x

Divide both sides by 2.

x 22

Thus mG 22 44 66.

Check It Out! Example 4

Find mH.

mH mG x

Isosc. Thm.

mH mG mF 180

Sum Thm.

Substitute the given values.

x x 48 180

Simplify and subtract 48 from both sides.

2x 132

Divide both sides by 2.

x 66

Thus mH 66

Check It Out! Example 5

Find mN.

mP mN

Isosc. Thm.

Substitute the given values.

(8y 16) 6y

Subtract 6y and add 16 to both sides.

2y 16

Divide both sides by 2.

y 8

Thus mN 6(8) 48.

The following corollary and its converse show the

connection between equilateral triangles and

equiangular triangles.

(No Transcript)

Example 6 Using Properties of Equilateral

Triangles

Find the value of x.

LKM is equilateral.

Equilateral equiangular

The measure of each of an equiangular is 60.

(2x 32) 60

Subtract 32 both sides.

2x 28

Divide both sides by 2.

x 14

Example 7 Using Properties of Equilateral

Triangles

Find the value of y.

NPO is equiangular.

Equiangular equilateral

Definition of equilateral .

5y 6 4y 12

Subtract 4y and add 6 to both sides.

y 18

Check It Out! Example 8

Find the value of JL.

JKL is equiangular.

Equiangular equilateral

Definition of equilateral .

4t 8 2t 1

Subtract 4y and add 6 to both sides.

2t 9

t 4.5

Divide both sides by 2.

Thus JL 2(4.5) 1 10.

Lesson Quiz Part I

Find each angle measure. 1. mR 2. mP Find

each value. 3. x 4. y 5. x

28

124

6

20

26

Homework

- Pg. 191 1-8, 12-15, 18, 26-33

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